Appendices
Tej Seth and Projeet Mukherjee
Figure 1: Histogram of Overall
Figure 2: Histogram of Shooting Rating
Figure 3: Histogram of Passing Rating
Figure 4: Histogram of Defending Rating
Figure 5: Histogram of Physicality Total
Figure 6: Histogram of Age
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Figure 7: Histogram of Height
Figure 8: Histogram of Contract Value
Figure 9: Scatter Plot of Contract Value and Overall
***
Figure 10: Scatter Plot of Age and Overall
Figure 11: Scatter Plot of Height and Overall
Figure 12: Scatter Plot of Shooting Rating and Overall
Figure 13: Scatter Plot of Defending Rating and Overall
Figure 14: Scatter Plot of Passing Rating and Overall
Figure 15: Boxplot of Overall Rating by Position
Figure 16: Interaction Terms
## Warning: The shape palette can deal with a maximum of 6 discrete values because
## more than 6 becomes difficult to discriminate; you have 15. Consider
## specifying shapes manually if you must have them.## Warning: Removed 2116 rows containing missing values (geom_point).
Figure 17: Building the Model Subsets
## model p rsq rss adjr2 cp
## 1 lg(VEUR) 2 0.785 47394 0.785 31497
## 2 A-lg(VEUR) 3 0.966 7552 0.966 997
## 3 A-lg(VEUR)-BPG 4 0.968 7019 0.968 590
## 4 A-D-lg(VEUR)-BPG 5 0.969 6790 0.969 418
## 5 A-PsT-PhT-lg(VEUR)-BPG 6 0.970 6643 0.970 306
## 6 A-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCB 7 0.970 6532 0.970 224
## 7 A-I(D-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCM 8 0.971 6471 0.971 179
## 8 A-I(D-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCM-l(VEUR):BPG 9 0.971 6419 0.971 142
## bic stderr
## 1 -7346 3.15
## 2 -16137 1.26
## 3 -16480 1.21
## 4 -16630 1.19
## 5 -16727 1.18
## 6 -16799 1.17
## 7 -16836 1.16
## 8 -16865 1.16
##
## Model variables with abbreviations
## model
## lg(VEUR) log(ValueEUR)
## A-lg(VEUR) Age-log(ValueEUR)
## A-lg(VEUR)-BPG Age-log(ValueEUR)-BestPositionGK
## A-D-lg(VEUR)-BPG Age-DefendingTotal-log(ValueEUR)-BestPositionGK
## A-PsT-PhT-lg(VEUR)-BPG Age-PassingTotal-PhysicalityTotal-log(ValueEUR)-BestPositionGK
## A-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCB Age-PassingTotal-PhysicalityTotal-log(ValueEUR)-BestPositionGK-log(ValueEUR):BestPositionCB
## A-I(D-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCM Age-I(DefendingTotal^2)-PassingTotal-PhysicalityTotal-log(ValueEUR)-BestPositionGK-log(ValueEUR):BestPositionCM
## A-I(D-PsT-PhT-lg(VEUR)-BPG-l(VEUR):BPCM-l(VEUR):BPG Age-I(DefendingTotal^2)-PassingTotal-PhysicalityTotal-log(ValueEUR)-BestPositionGK-log(ValueEUR):BestPositionCM-log(ValueEUR):BestPositionGK
##
## model with largest adjr2
## 8
##
## Number of observations
## 4791Figure 18: VIF Scores for the Model
## Age Height DefendingTotal PassingTotal
## 2.018873 1.955955 5.406309 4.382201
## PhysicalityTotal log(ValueEUR) BestPositionCB BestPositionCDM
## 3.081032 3.043478 5.662960 2.206623
## BestPositionCF BestPositionCM BestPositionGK BestPositionLB
## 1.037259 1.635677 2.493684 1.840696
## BestPositionLM BestPositionLW BestPositionLWB BestPositionRB
## 1.378816 1.112406 1.241394 1.874169
## BestPositionRM BestPositionRW BestPositionRWB BestPositionST
## 1.644086 1.212457 1.283539 3.402799Figure 19: Final Model
##
## Call:
## lm(formula = Overall ~ Age + Height + DefendingTotal + I(DefendingTotal^2) +
## PassingTotal + PhysicalityTotal + log(ValueEUR) * BestPosition,
## data = fifa_smallest)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0714 -0.6767 -0.0197 0.6420 6.0279
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) -16.5067118 0.8452714 -19.528
## Age 0.5457429 0.0052404 104.141
## Height -0.0035143 0.0033896 -1.037
## DefendingTotal -0.0093293 0.0093857 -0.994
## I(DefendingTotal^2) 0.0001855 0.0001076 1.724
## PassingTotal 0.0523969 0.0035790 14.640
## PhysicalityTotal 0.0251204 0.0030429 8.255
## log(ValueEUR) 4.6208428 0.0429695 107.538
## BestPositionCB 1.4468696 0.7637876 1.894
## BestPositionCDM 0.7162297 0.9073359 0.789
## BestPositionCF 7.0596134 3.9587830 1.783
## BestPositionCM 2.0868579 0.9673519 2.157
## BestPositionGK 4.7261300 0.7687762 6.148
## BestPositionLB 0.4643580 1.0650687 0.436
## BestPositionLM -0.1970164 1.0786120 -0.183
## BestPositionLW 3.9216465 2.8803753 1.362
## BestPositionLWB 0.9648900 2.0280248 0.476
## BestPositionRB 0.4388699 1.1256065 0.390
## BestPositionRM -2.0311614 0.9175616 -2.214
## BestPositionRW 2.5732131 1.4765286 1.743
## BestPositionRWB -2.3085406 1.8312908 -1.261
## BestPositionST -0.3106739 0.7749704 -0.401
## log(ValueEUR):BestPositionCB -0.0666918 0.0563953 -1.183
## log(ValueEUR):BestPositionCDM -0.0553243 0.0655927 -0.843
## log(ValueEUR):BestPositionCF -0.5328990 0.2620185 -2.034
## log(ValueEUR):BestPositionCM -0.1731170 0.0678564 -2.551
## log(ValueEUR):BestPositionGK -0.2705871 0.0557554 -4.853
## log(ValueEUR):BestPositionLB -0.0108126 0.0768752 -0.141
## log(ValueEUR):BestPositionLM 0.0237498 0.0766487 0.310
## log(ValueEUR):BestPositionLW -0.2369725 0.2027724 -1.169
## log(ValueEUR):BestPositionLWB -0.0387435 0.1439129 -0.269
## log(ValueEUR):BestPositionRB -0.0086384 0.0815002 -0.106
## log(ValueEUR):BestPositionRM 0.1556315 0.0656485 2.371
## log(ValueEUR):BestPositionRW -0.1590528 0.1047462 -1.518
## log(ValueEUR):BestPositionRWB 0.2023012 0.1308002 1.547
## log(ValueEUR):BestPositionST 0.0403280 0.0548222 0.736
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## Age < 0.0000000000000002 ***
## Height 0.2999
## DefendingTotal 0.3203
## I(DefendingTotal^2) 0.0847 .
## PassingTotal < 0.0000000000000002 ***
## PhysicalityTotal < 0.0000000000000002 ***
## log(ValueEUR) < 0.0000000000000002 ***
## BestPositionCB 0.0582 .
## BestPositionCDM 0.4299
## BestPositionCF 0.0746 .
## BestPositionCM 0.0310 *
## BestPositionGK 0.000000000851 ***
## BestPositionLB 0.6629
## BestPositionLM 0.8551
## BestPositionLW 0.1734
## BestPositionLWB 0.6343
## BestPositionRB 0.6966
## BestPositionRM 0.0269 *
## BestPositionRW 0.0814 .
## BestPositionRWB 0.2075
## BestPositionST 0.6885
## log(ValueEUR):BestPositionCB 0.2370
## log(ValueEUR):BestPositionCDM 0.3990
## log(ValueEUR):BestPositionCF 0.0420 *
## log(ValueEUR):BestPositionCM 0.0108 *
## log(ValueEUR):BestPositionGK 0.000001254323 ***
## log(ValueEUR):BestPositionLB 0.8882
## log(ValueEUR):BestPositionLM 0.7567
## log(ValueEUR):BestPositionLW 0.2426
## log(ValueEUR):BestPositionLWB 0.7878
## log(ValueEUR):BestPositionRB 0.9156
## log(ValueEUR):BestPositionRM 0.0178 *
## log(ValueEUR):BestPositionRW 0.1290
## log(ValueEUR):BestPositionRWB 0.1220
## log(ValueEUR):BestPositionST 0.4620
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.148 on 4755 degrees of freedom
## Multiple R-squared: 0.9716, Adjusted R-squared: 0.9714
## F-statistic: 4646 on 35 and 4755 DF, p-value: < 0.00000000000000022Figure 20: Residuals vs. Fitted Plot
Figure 21: QQ Plot
